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Short-Term Traffic Prediction Using Rainfall
Haiyun Lu SAP Research and Innovation, Singapore
Email: [email protected]
Abstract—We propose an approach to predict short-term
travel time for expressways using rainfall data. The rainfall
rate is quantitatively related to the travel time and is used to
perform the prediction. The proposed approach is
experimented on real data collected in Singapore. Results
show that it performs better compared to three baseline
approaches. It is also shown that the proposed approach is
applicable and effective in Singapore.
Index Terms—intelligent transportation systems, traffic
prediction, travel time prediction, weather correlation,
impulse response.
I. INTRODUCTION
Traffic forecasting is an important component in an
intelligent transportation system in the concept of smart
city. Since decades ago, research effort has been devoted
to various traffic prediction models and methods.
The traffic prediction problem can be classified into
two categories in terms of time scale: long-term and
short-term [1]. Long-term prediction targets for monthly
or even yearly information of traffic states and it is used
for long-term transportation planning. Short-term
prediction aims for the near future, such as 15 minutes
later. It can be used by experts to guide traffic flow and
manage congestion. It may also be available to common
citizens of the city to help them plan their trips wisely. By
definition, short-term traffic forecasting is the process to
predict key traffic parameters such as speed, flow,
occupancy, or travel time with a forecasting horizon
typically ranging from five to thirty minutes at specific
locations, given real-time and historical traffic data from
relevant surveillance stations [2].
Traffic prediction methods often employ statistical
methodologies and there are two major types of models:
parametric model and non-parametric model. Parametric
models include random walk, historical average [3],
linear regression [4], Kalman filter [5], [6],
autoregressive moving average [7]-[9]. These methods
derive a mathematical function between history states and
predicted states. Non-parametric models include neural
networks [10]-[12], Bayesian networks [13], K-nearest
neighbor [14], [15]. These methods analyze
characteristics of traffic data and approximate the model
with a certain precision using a growing dataset.
Other than historical traffic data, weather information
is also an important factor of traffic forecasting. Various
Manuscript received February 7, 2014; revised April 25, 2014.
studies show that bad weather conditions, such as rain,
snow, fog, ice, flooding, wind and high temperature,
generally result in more accidents on roads [16]-[19]. It is
also shown that heavy precipitation conditions have
impact on traffic speed, capacity, volume, intensity, flow
and travel time [20]-[27]. In particular, rain condition is
reported to cause speed reduction by 6% to 12% in
different locations [23], [27]. Heaving rainfall condition
decreases the visibility and causes wet surface on roads,
so road users will slow down their vehicles in order to
drive safely. Given such correlation between rainfall and
traffic, it is important to include rainfall in the traffic
prediction system for rainy places.
In this paper, we propose to predict short-term travel
time for expressways using rainfall data. Travel time on
expressways in Singapore is used for this study.
Singapore has a tropical rainforest climate where rainfall
is very frequent throughout the year. Thus the proposed
traffic prediction approach is ideally applicable to the
data obtained in Singapore.
II. PROPOSED APPROACH
In our approach, travel time on the expressway is
predicted using rainfall data. We build our solution based
on one assumption, that is, there is a quantitative
relationship between rainfall rate and traffic condition. As
mentioned previously, when there is a heavy rain, drivers
will slow down to keep it safe. This is generally
considered as a causal correlation. Fig. 1 shows the plot
of rainfall rate and travel time for a segment of
expressway on a typical weekday. We can see that travel
time increases at morning and evening peak hours, which
is generally expected. However, it also increases around
15:00 (off peak hour) on that day, which is overlapping
with a raining period around the same time.
Figure 1. Rainfall rate and travel time.
International Journal of Signal Processing Systems Vol. 2, No. 1 June 2014
©2014 Engineering and Technology Publishing 70doi: 10.12720/ijsps.2.1.70-73
To demonstrate the impact of the rainfall on traffic, we
constructed the cross-correlations function between travel
time and rainfall rate, as in (1), where is 24 hours, is
time, ( ) is the deviation from normal travel time and
( ) is the rainfall rate.
∫ ( ) ( )
(1)
The deviation ( ) is computed as in (2), where ( ) is
the travel time at time and ̅( ) is the historical average
of the travel time.
( ) ( ) ̅( ) (2)
The peak value of the cross-correlation is located at the
delay necessary to align the two time series. Fig. 2
shows a histogram of the location of the largest peak
found in the cross-correlation function. The largest peak
is at delay 0-15 minutes. It implies that the rainfall has a
near-immediate impact on the travel time.
Figure 2. Histogram of location of the largest peak in cross-correlation
of travel time and rainfall rate.
Given the quantitative relationship between rainfall
and traffic, we model the travel time as a linear system
adapted from Dailey’s work [28]. Equation (3) of the
system is with two components: the normal travel time
and the contribution from the rainfall. The normal travel
time ̅( ) is the historical average of travel time at time of the day. The rainfall contribution is approximated by
convolving the impulse response function ( ) with the
rainfall rate ( ).
( ) ̅( ) ∫ ( ) ( ) (3)
The impulse response function ( ) needs to be
derived from training data. To compute , we re-write the
above equation and apply Fourier transform:
( ) ∫ ( ) ( ) (4)
( ) ( ) ( ) (5)
is the Fourier transform of the travel time deviation
, is the Fourier transform of the impulse response
function , and is the Fourier transform of the rainfall
rate . After multiplying the complex conjugate value of
, we can rewrite the equation to compute .
(6)
(7)
Then the impulse response function can be
approximated by the inverse Fourier transform of ,
where and are the power spectrum. Fig. 3
shows a typical impulse response function for an
expressway.
Figure 3. Impulse response function.
After obtaining the impulse response function, travel
time can be predicted by the linear system model. By
adding weight parameter , the system, as in (8), is more
tolerable to false contributions due to short or light rain.
( ) ̅( ) ∫ ( ) ( ) (8)
{ if ̅ if ̅ and ̅ otherwise.
(9)
where ̅ is the average of the rainfall rates used in the
convolution, and are empirically determined
thresholds.
In the next section, the proposed approach is applied
on real data collected in Singapore.
III. EXPERIMENT
A. Data Collection
Travel time data with 5 minutes interval are collected
for eight expressways (AYE, BKE, CTE, ECP, KJE, PIE,
SLE, and TPE) from September 2013 to February 2014.
Travel time is measured between consecutive exits of the
expressway. In total there are 183 segments of the
expressway. The travel time data are published by the
Land Transport Authority of Singapore on public website
(mytransport.sg). Fig. 4 shows historical average of travel
time for a typical expressway segment on weekday.
Figure 4. Average travel time on weekdays.
International Journal of Signal Processing Systems Vol. 2, No. 1 June 2014
©2014 Engineering and Technology Publishing 71
Rainfall data are collected for the same time period as
travel time data. They are published by the National
Environment Agency of Singapore on their public
website (app2.nea.gov.sg). The rainfall data are obtained
from weather radar, derived into image visualization (see
Fig. 5) and published at every 5-10 minutes interval.
Figure 5. Rain map published on app2.nea.gov.sg.
Rainfall rate data have to be reversely derived from the
image visualization using the Doppler radar reflectivity:
(
)
(10)
where is the rainfall rate, is the reading taken from
the image visualization, =0.097 and =0.997 are
empirically determined parameters. The rainfall rate
corresponding to a particular expressway segment is
approximated by the average of rainfall rates in the area
of this segment.
B. Results and Comparison
To predict the traffic, the impulse response function
needs to be derived from training data. We use the data
collected from September to November 2013 as training
data. Impulse response function is computed for each
segment of the expressways.
After learning the impulse response functions, we
apply the prediction approach to predict travel time given
the rainfall data from December 2013 to February 2014.
The prediction interval is chosen to be 15 minutes, which
is the maximum interval presented in the data collected.
The results are measured by the mean absolute
percentage error (MAPE) and the root mean square error
(RMSE):
∑
| ̂ |
(11)
√∑ ( ̂ )
(12)
where ̂ is predicted travel time at time and is actual
travel time at time . Table I lists the final results averaged from the
experiment results for all 183 expressway segments. The
results are compared to three baseline prediction
approaches mentioned in the studies [8], [9]. The first
baseline approach models the traffic as random walk,
then the forecast for next state is simply the most recent
state, that is, ̂ . The second baseline approach
predicts the next state by using previously observed
historical average of the travel time, that is, ̂ ̅ . The
last baseline approach calculates the prediction with a
smoothing parameter, that is, ̂ ( ) ̂ where =0.2. These baseline approaches are applied to
the same dataset and evaluated using the same measure.
TABLE I. EXPERIMENT RESULTS
Approach MAPE RMSE
Random walk forecast 5.372% 0.383
Historical average forecast 7.357% 0.435
Smoothed historical average forecast 5.347% 0.394
Our proposed approach 4.669% 0.339
From the comparison, it is clear that the proposed
approach achieves better experiment results. Fig. 6 shows
two examples of the predicted travel time versus the
actual travel time plotted for one day. It shows that the
increase of travel time can be effectively predicted for
raining periods at off peak hours.
Figure 6. Predicted travel time versus actual travel time.
IV. CONCLUSION
In this paper, we presented an approach to predict
short-term travel time for expressways using rainfall data.
We use an impulse response function to quantitatively
relate the rainfall rate to travel time and use a weighted
linear system to perform the prediction. The experiment
is conducted on real data collected in Singapore. The
results show that the proposed approach achieves lower
errors compared to three baseline approaches. It is also
shown that the proposed approach is applicable and
effective in Singapore.
International Journal of Signal Processing Systems Vol. 2, No. 1 June 2014
©2014 Engineering and Technology Publishing 72
However, there is still room for further research. For
example, some parameters are empirically determined. It
could be a challenging task to find suitable values for
those parameters in practice. Another issue is that the
proposed model may be only applicable to rainy places.
The prospect is to combine this model with others to
enhance the flexibility and robustness.
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Haiyun Lu obtained PhD in Computer Science from National University of Singapore in 2012, and Bachelor of Computing from the
same university.
She is currently a Researcher with SAP Research & Innovation in Singapore. Her research interests include computer vision and machine
learning.
International Journal of Signal Processing Systems Vol. 2, No. 1 June 2014
©2014 Engineering and Technology Publishing 73